It worked, thank you very much.
It really improves a lot the integration of Zotero with other note taking apps.

I could transfer to Obsidian or Evernote by:
- Drag and drop (or Ctrl+Shift+C > Ctrl+V ) a note with annotations
- Drag and drop the annotations directly from the Zotero PDF Reader
- Copy (Ctrl+C) - Paste (Ctrl+v) annotations from the Zotero PDF Reader

But:
- If I Copy (Ctrl+C) - Paste (Ctrl+v) the annotation from the note, I only get the text of the annotation. I am not sure if it should also carry the links? The Ctrl+Shift+C > Ctrl+V behaviour still copies the whole note, even when some text is selected.
- If I want to get the back link to an item in my library when transferring to another app, I still need to get the link to a Zotero note first, and then transfer the whole note to the target app. I cannot get it directly, or select only that link from the note.
- If I drag and drop an item into a note, I get a citation with back link. But if I do the same to an external note taking app, I get the Bibliography information. I find it confusing. I would expect to get the same everywhere.
- I am a bit confused also at what is the Quick Copy doing. It seems that Quick Copy of an item is controlled by the translators listed in the "Item Format" section of the preferences, and the Notes/Annotations controlled by the Note Templates. And that Quick Copy Ctrl+Shift+C is doing the same as drag and drop... With the exception of the previous point, when doing drag and drop of an item into a Zotero note. I was hoping that Quick Copy of notes and items from the library would be more consistent.

The new functionality seems to be blocked by the Better BibTeX add-on. I will report to its GitHub.
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From mjthoraval

"But if I do the same to an external note taking app, I get the Bibliography information." -> I am experimenting the same behaviour. Would be nice to drag and drop to libreoffice with Zotero links.

"The new functionality seems to be blocked by the Better BibTeX add-on. I will report to its GitHub." -> I got a similar problem, to my knowledge a similar issue has been reported in Github some times ago https://github.com/retorquere/zotero-better-bibtex/issues/2155 and Zotero forum https://forums.zotero.org/discussion/98245/dragging-articles-to-collections-is-slow/p1

Hoping the best for what comes next!

This is now available in Zotero 6.0.16.

@mjthoraval:

If I Copy (Ctrl+C) - Paste (Ctrl+v) the annotation from the note, I only get the text of the annotation. I am not sure if it should also carry the links?

It's supposed to include the links if a full annotation or citation is selected, and does for Markdown, but that doesn't seem to be working at the moment for rich-text mode. We'll fix that. Partial selections would copy regular text.

If I want to get the back link to an item in my library when transferring to another app, I still need to get the link to a Zotero note first, and then transfer the whole note to the target app. I cannot get it directly, or select only that link from the note.

And @rhysie21:

I would love an option to just directly copy the link to the annotation or page of the document.

Zotero has never supported direct copying of zotero:// links for items before — only plugins have — but now that we're including these in exported notes, it probably makes sense for us to add support for it. We'll think about how best to do that.

For the rest:

If I drag and drop an item into a note, I get a citation with back link. But if I do the same to an external note taking app, I get the Bibliography information. I find it confusing. I would expect to get the same everywhere.

I was hoping that Quick Copy of notes and items from the library would be more consistent.

The consistency is that you get the default behavior that makes the most sense for what you're doing. Zotero has automatically generated bibliography entries when dragging one or more items to an external text field forever — it's a signature, well-loved feature of Zotero and one that we're certainly not going to change. But that makes no sense in a Zotero note, where most people don't need flat bibliography entries but where live citations that dynamically link back to the item and that can remain active Zotero citations in a word processor document are much more useful.

@dstillman

"Zotero has never supported direct copying of zotero:// links for items before — only plugins have — but now that we're including these in exported notes, it probably makes sense for us to add support for it. We'll think about how best to do that."

+1 This would be fantastic. Copying the extracted comments to Word and then being able to Ctrl+Click to jump right into the original document was a very helpful part of my prior ZotFile workflow for annotated bibliographies.